Atomic decompositions of vector-valued weak Musielak-Orlicz martingale spaces and applications

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• 作者：Anming Yang ^{amyang14@fudan.edu.cn}
• 关键词：Musielak&ndash ; Orlicz function ; Banach space ; Vector-valued martingale ; Atomic decomposition ; Martingale inequality
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：670-681
• 全文大小：327 K
• 卷排序：449

文摘

In this paper, some vector-valued weak martingale Hardy spaces of Musielak–Orlicz type are introduced, and several atomic decompositions are established for them. As applications of the atomic decompositions, a sufficient condition for sublinear operators defined on vector-valued weak Musielak–Orlicz martingale spaces to be bounded is given. Using the sufficient condition, some martingale inequalities are deduced. These results closely depend on the geometrical properties of the Banach space in which the martingales take values. The results obtained here generalize the corresponding known results of scalar-valued and vector-valued weak martingale Hardy spaces.